TY - JOUR

T1 - Many triangulated odd-dimensional spheres

AU - Nevo, Eran

AU - Santos, Francisco

AU - Wilson, Stedman

N1 - Publisher Copyright:
© 2015, Springer-Verlag Berlin Heidelberg.

PY - 2016/4/1

Y1 - 2016/4/1

N2 - It is known that the (Formula presented.) -sphere has at most (Formula presented.) combinatorially distinct triangulations with n vertices, for every (Formula presented.). Here we construct at least (Formula presented.) such triangulations, improving on the previous constructions which gave (Formula presented.) in the general case (Kalai) and (Formula presented.) for (Formula presented.) (Pfeifle–Ziegler). We also construct (Formula presented.) geodesic (a.k.a. star-convex) n-vertex triangulations of the (Formula presented.) -sphere. As a step for this (in the case (Formula presented.)) we construct n-vertex 4-polytopes containing (Formula presented.) facets that are not simplices, or with (Formula presented.) edges of degree three.

AB - It is known that the (Formula presented.) -sphere has at most (Formula presented.) combinatorially distinct triangulations with n vertices, for every (Formula presented.). Here we construct at least (Formula presented.) such triangulations, improving on the previous constructions which gave (Formula presented.) in the general case (Kalai) and (Formula presented.) for (Formula presented.) (Pfeifle–Ziegler). We also construct (Formula presented.) geodesic (a.k.a. star-convex) n-vertex triangulations of the (Formula presented.) -sphere. As a step for this (in the case (Formula presented.)) we construct n-vertex 4-polytopes containing (Formula presented.) facets that are not simplices, or with (Formula presented.) edges of degree three.

UR - http://www.scopus.com/inward/record.url?scp=84930257550&partnerID=8YFLogxK

U2 - 10.1007/s00208-015-1232-x

DO - 10.1007/s00208-015-1232-x

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AN - SCOPUS:84930257550

SN - 0025-5831

VL - 364

SP - 737

EP - 762

JO - Mathematische Annalen

JF - Mathematische Annalen

IS - 3-4

ER -